Representations of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$
Studia Mathematica, Tome 142 (2000) no. 2, pp. 135-148
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We give a representation of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^∞(ℝ^N) ∩ H^{k,2}(ℝ^N)$ is isomorphic to the sequence space $s^{ℕ} ∩ l^2(l^2)$, thereby showing that the isomorphy class does not depend on the dimension N if p=2.
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author = {A. Albanese and V. Moscatelli},
title = {Representations of the spaces $C^\ensuremath{\infty}(\ensuremath{\mathbb{R}}^N) \ensuremath{\cap} H^{k,p}(\ensuremath{\mathbb{R}}^N)$},
journal = {Studia Mathematica},
pages = {135--148},
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A. Albanese; V. Moscatelli. Representations of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$. Studia Mathematica, Tome 142 (2000) no. 2, pp. 135-148. doi: 10.4064/sm-142-2-135-148
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